1. Field of the Invention
This invention relates to the field of electrical devices. More specifically, the invention comprises a method for controlling effective impedance in a superconducting cable.
2. Description of the Related Art
Recent developments have allowed the commercialization of high-temperature superconducting (“HTS”) power distribution cables. These cables have a much higher power density that conventional transmission lines. They also undergo substantially lower resistive losses. The application of HTS cables to existing power grids is therefore expected in the near future.
While there are several designs for HTS cables, the currently favored approach uses a cold-dielectric coaxial cable with HTS shielding. FIG. 1 illustrates a typical construction for such a cable, labeled as HTS cable 10. It includes several concentric layers. Structural core 12 lies at its center. This component may be stranded copper, similar to that found in conventional electrical transmission lines. However, its function is primarily to carry the tensile mechanical load of the cable. Though it may carry some electrical current, this is incidental.
The next layer is HTS conductor tape 14. This carries the electrical line current of the HTS cable. The next layer is high voltage (“HV”) dielectric 16. HTS shield tape 18 is wrapped over HV dielectric 16. As will be explained subsequently, a substantial voltage potential can exist between HTS conductor tape 14 and HTS shield tape 18. The dielectric prevents a short circuit between the two.
Liquid nitrogen coolant 20 flows over HTS shield tape 18. This layer of cooling fluid is typically pumped under pressure to cause a steady flow. Thus, everything inside the layer of liquid nitrogen is immersed in a cryogenic “bath.” The temperature of these components is maintained at or slightly above the temperature of the liquid nitrogen. The liquid nitrogen is contained by inner cryostat wall 22. A gap—in which a vacuum is generally maintained—exists between inner cryostat wall 22 and outer cryostat wall 24. This gap may sometimes be filled by an insulating material having extremely low thermal conductivity. Protective cover 26 overlies the entire assembly and provides additional mechanical strength.
Those skilled in the art will know that a variety of construction techniques are used to create HTS cables. The one shown in FIG. 1 is only one example. Additional components can be added. For instance, a copper winding can be added over HTS shield tape 18 in order to add additional mechanical strength. The methods disclosed herein are applicable to virtually any type of cable construction. Thus, the details shown in FIG. 1 should be viewed only as an example.
Those skilled in the art will be familiar with the concept of impedance. Impedance is a very important principle in the analysis of alternating currents. It can be understood by reviewing the equations relating voltage to current in resistors, inductors, and capacitors. These equations are as follows:
                    V        =                                            RI                                                                                                                              (        resistor        )                                V        =                                                                              j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  LI                                ;                                                                                                                                                      (          inductor          )                ⁢                                  ⁢        and                                V        =                                                                              (                                                                          ⁢                                      1                                                                                                              ⁢                                              j                        ⁢                                                                                                  ⁢                        ω                        ⁢                                                                                                  ⁢                        C                                                                              )                                ⁢                                                                  ⁢                I                                                                                                                                                      (          capacitor          )                .            All of these equations can be expressed as V=ZI, where “Z” stands for impedance.
The impedance of an HTS cable is a significant factor when such a cable is integrated into a power distribution network. Power distribution networks typically involve parallel connections of multiple transmission lines. This serves to create redundancy, as well as providing the ability to route capacity where it is needed.
FIG. 2 shows a simple parallel power grid 28. Five lines are involved. A first set of two conventional power lines goes from point J to Point K to Point M. A second set of two conventional lines goes from Point J to Point L to Point M. HTS cable 10 has been routed directly from point J to Point M. The distance for each segment (in kilometers) is shown in the figure. 600 MW is fed into Point J and extracted from Point M (ignoring resistance losses).
The resistance and inductance of the HTS cable is drastically lower than the conventional power lines. The following table provides these properties:
TABLE ITypeResistance (Ω/km)Inductance (mH/km)HTS0.00010.06Conventional0.081.26
Thus, with no impedance modification to the HTS cable, it will be the path of least resistance for the current flowing into the parallel power grid. The result is that the HTS cable will carry 564 MW, while the two conventional cables will carry 18.1 MW (for the cable in the top part of FIG. 2) and 17.9 MW.
The reader will therefore understand that if the HTS cable is connected in parallel with conventional lines, the vast majority of the current will “dump” into the HTS cable. The current capacity of the conventional lines will likewise be under-utilized.
In addition to the concern of under-utilizing existing transmission lines, this phenomenon is troublesome for the HTS cable as well. The HTS cable only maintains its superconductivity if the temperature of the superconductor is maintained below a certain threshold. Increasing the current through the cable increases the resistance loss, which drives up the temperature. Driving up the temperature, as is commonly known, increases the cable's resistance (even while below the temperature threshold where superconductivity is lost). This thermal load can eventually overwhelm the liquid cooling system, resulting in a self-accelerating problem: More load causes more heat, which causes more resistance, which causes still more heat, etc.
If the cooling system is overwhelmed, the HTS cable's temperature will rise above the superconductivity threshold. At that point, resistance will spike dramatically (often referred to as “quenching”). The HTS cable may physically fail. Even if it does not, a sudden surge of current will transfer to the conventional lines, possibly causing them to fail.
Thus, in a grid like the one shown in FIG. 2, the inability to direct current flows in desired ratios is a substantial disadvantage. Having the ability to control the effective impedance of the HTS cable is therefore desirable.